A chemical reaction is where atoms are rearranged to produce a new substance.

Evidence of a chemical reaction:
Color change
change in odor
precipitate forms
appearance of a gas

the following two videos show chemical reactions.

The first video show potassium permanganate and glycerine being combined. This reaction is an exothermic reaction.

http://youtu.be/49MaJ0NtQAE

The second video shows what happens when lead nitrate and sodium iodide are mixed. You will see the formation of a precipitate.

http://youtu.be/0oOjoE0wvzc